What substrate will soften my very hard water - peat or something else? I read on planted about an ADA substrate?

u could use peat in ur filter rather than substrate.

How does that work?

Peat moss softens water and reduces its hardness (GH). The most effective way to soften water via peat is to aerate water for 1-2 weeks in a bucket containing peat moss. For example, get a (plastic) bucket of the appropriate size. Then, get a large quantity of peat (a gallon or more), boil it (so that it sinks), stuff it in a pillow case, and place it in the water bucket. Use an air pump to aerate it. In 1-2 weeks, the water will be softer and more acidic. Use this aged water when making partial water changes on your tank.

Peat can be bought at pet shops, but it is expensive. It is much more cost-effective to buy it in bulk at a local gardening shop. Read labels carefully! You don't want to use peat containing fertilizers or other additives.

Although some folks place peat in the filters of their tanks, the technique has a number of drawbacks. First, peat clogs easily, so adding peat isn't always effective. Second, peat can be messy and may cloud the water in your tank. Third, the exact quantity of peat needed to effectively soften your water is difficult to estimate. Using the wrong amount results in the wrong water chemistry. Finally, when doing water changes, your tank's chemistry changes when new water is added (it has the wrong properties). Over the next few days, the chemistry changes as the peat takes effect. Using aged water helps ensure that the chemistry of your tank doesn't fluctuate while doing water changes.